## Rounding to Significant Digits Once you’ve identified the number of significant digits in a value or calculation, you often need to **round** the result before reporting it. Rounding to significant digits helps ensure that your answer reflects the **precision of your tools** and the **certainty of your measurements**. ### General Steps to Round to Significant Digits 1. **Count significant digits** from the **first non-zero digit** (not just decimal places). 2. **Look at the digit just after** the last significant digit you want to keep. 3. If that digit is **5 or more**, round the last digit **up**. 4. If that digit is **less than 5**, leave the last digit **unchanged**. 5. All digits after the rounded digit are **removed**. ### Examples #### Example 1: Round 3.786 to 2 significant digits - First 2 significant digits: 3 and 7 - Next digit is 8 → round up - Result: **3.8** #### Example 2: Round 0.004827 to 3 significant digits - First 3 significant digits: 4, 8, 2 - Next digit is 7 → round up - Result: **0.00483** #### Example 3: Round 1.249 to 2 significant digits - First 2 significant digits: 1 and 2 - Next digit is 4 → round down - Result: **1.2** ## Using Scientific Notation for Large or Small Values When rounding very large or small numbers, scientific notation helps keep the number readable while preserving significant digits. #### Example 4: Round 231000 to 2 significant digits - First 2 digits: 2 and 3 - Result: $2.3 \times 10^5$ #### Example 5: Round 0.0006784 to 2 significant digits - First 2 digits: 6 and 7 - Next digit is 8 → round up - Result: $6.8 \times 10^{-4}$ ## Electrical Examples |Quantity|Raw Value|Rounded (3 Sig Figs)|Why| |---|---|---|---| |Voltage|13.8761 V|13.9 V|6 is next → round up| |Resistance|0.04732 Ω|0.0473 Ω|2 is next → leave it| |Current|4.006 A|4.01 A|6 rounds 0 up to 1| |Energy|25800 J|$2.58 \times 10^4$ J|Scientific notation helps show sig figs clearly| ## Summary - Round using the **significant digit count**, not decimal places - Always start counting from the **first non-zero digit** - Scientific notation can help maintain clarity when rounding large/small numbers - Rounding is part of professional test reporting and measurement documentation